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Stability properties of differential-algebraic equations and spin-stabilized discretizations

Please always quote using this URN:urn:nbn:de:0296-matheon-3574
  • Classical stability properties of solutions that are well-known for ordinary differential equations (ODEs) are generalized to differential-algebraic equations (DAEs). A new test equation is derived for the analysis of numerical methods applied to DAEs with respect to the stability of the numerical approximations. Morevover, a stabilization technique is developed to improve the stability of classical DAE integration methods. The stability regions for these stabilized discretization methods are determined and it is shown that they much better reproduce the stability properties known for the ODE case than in the unstabilized form. Movies that depict the stability regions for several methods are included for interactive use.

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Metadaten
Author:Peter Kunkel, Volker Mehrmann
URN:urn:nbn:de:0296-matheon-3574
Referee:Christof Schütte
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2006/09/11
Release Date:2006/12/09
Tag:
Institute:Technische Universität Berlin
MSC-Classification:34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Dxx Stability theory [See also 37C75, 93Dxx] / 34D20 Stability
34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Dxx Stability theory [See also 37C75, 93Dxx] / 34D23 Global stability
65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L20 Stability and convergence of numerical methods
65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L80 Methods for differential-algebraic equations
Preprint Number:356
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